非强占型优先权的M/M/N可修排队系统

研究一类带有非强占型优先权、服务台忙时与闲时故障率不同的M/M/N可修排队系统,在画出系统状态转移图的基础上,得到系统瞬态概率密度满足的微分方程组。利用拟生灭过程的方法求出系统稳态条件,并在此基础上得到系统的稳态平衡方程组。通过对稳态方程组的分析得到系统中关键的N(N+1)/2个稳态概率值的求解思路,使用Mathematica软件编程实现了稳态概率值的求取过程,并举出一个具体实例。在得到稳态概率值的基础上给出了有效服务台数的稳态分布、稳态队长的母函数这两个系统指标。

M/M/N repairable queue system under nonpreemptive priority

To study the M/M/N repairable queue system with one repairman and nonpreemptive priority,in which the rates of server breakdown are different between busy time and idle time,the differential equations of this system are obtained by receiving the state transition diagram.By using the QBD(quasi birth and death process) method,the steady-state condition is got,and then the steady-state balanced equations are obtained.By analysing,the thinking of solving the key steady probability is got.Because of the complexity of calculating the steady probability by handwork when N≥2,the steady probability,can be obtained by using Mathematica software,and a numberical example is given.On the basis of deriving the steady probability,two indices,the steady state distribution of the number of effective servers and the moment generating function of the steady state queue length,are also given.